If the system of equations \((\lambda -1)x+(\lambda -4)y+\lambda z=5\\ \lambda x+(\lambda -1)y+(\lambda -4)z=7\\ (\lambd…

If the system of equations

\((\lambda -1)x+(\lambda -4)y+\lambda z=5\\ \lambda x+(\lambda -1)y+(\lambda -4)z=7\\ (\lambda +1)x+(\lambda +2)y-(\lambda +2)z=9\)

has infinitely many solutions, then \({\lambda }^{2}+\lambda\) is equal to

[JEE Main 2025, 23 Jan (Shift 1)]